The Senate Judiciary Committee gave final approval Tuesday to a sweeping immigration reform bill, setting up a debate on the Senate floor for early June.

Three Republicans joined 10 Democrats to support the bill, which would create a pathway to citizenship for 11 million undocumented immigrants, invest billions in new border security measures and overhaul the legal immigration system.

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The landmark legislation easily passed the Judiciary Committee, giving reform its best chance in six years on the Senate floor. Yet even if the bill clears the Senate, the GOP-controlled House isn’t likely to take it up in its current form.

The vote came after the committee deliberated for five days and considered more than 200 amendments. But the Gang of Eight, which drafted the legislation, held together and fended off all but minor changes to the bill.

“This is a big step forward,” said Sen. Chuck Schumer (D-N.Y.), a leader of the Gang. “We got a good vote in committee, we expanded our little group to another vote, and the feeling is very strong here. I think we gained some momentum today. I really do.”

Schumer and Sen. Jeff Flake (R-Ariz.) told reporters that they remained hopeful that the bill could pick up 70 votes on the Senate floor.

“I think it’s possible,” said Flake, another Gang member. “We got a lot of hard work to do. A lot of hard work.”

The committee room, which was packed with reform proponents, erupted in applause and cheers of “Yes, we can” after the final vote. Democratic senators posed for pictures with supporters and received a succession of high fives and hugs.

President Barack Obama issued a statement congratulating the committee and urging the Senate to take up the bill “at the earliest possible opportunity.”

“The process for considering this legislation has been open and inclusive with multiple hearings, and more than a hundred amendments were considered and adopted, in many cases with bipartisan support,” Obama said. “None of the Committee members got everything they wanted, and neither did I , but in the end, we all owe it to the American people to get the best possible result over the finish line.”

Senate leaders hope to begin considering the bill following the Memorial Day recess in June. That prospect got a boost on Tuesday when Minority Leader Mitch McConnell (R-Ky.) said he would not block debate from starting on the floor.

House leaders want their members to put forward their own version of immigration reform, which will be more conservative than the Senate bill. A bipartisan group of House negotiators announced an agreement last week on reform principles, but the lawmakers are struggling to finalize the deal.